443edo: Difference between revisions

Line 1:

== Theory ==

~~443et~~ tempers out ~~67108864/66976875,~~ [[6144/6125]] ~~and~~ [[32805/32768]] in the 7-limit; ~~806736/805255, 35156250/35153041, 759375/758912, [[131072/130977]],~~ [[540/539]]~~, 184549376/184528125~~, [[5632/5625]], [[8019/8000]], ~~160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172~~ and ~~20614528~~/~~20588575~~ in the 11-limit.

443edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1|5]] is quite large. To start with, the [[patent val]] {{val| 443 702 '''1029''' '''1244''' '''1533''' }} as well as the 443cde [[val]] {{val| 443 702 '''1028''' '''1243''' '''1532''' }} are worth considering.

===Prime harmonics===

Using the patent val, the equal temperament [[tempering out|tempers out]] [[6144/6125]], [[32805/32768]], and 67108864/66976875 in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]], and [[131072/130977]] in the 11-limit. It [[support]]s [[hemischis]], the 130 & 313 temperament.

=== Prime harmonics ===

===Subsets and supersets===

=== Subsets and supersets ===

443edo is the 86th [[prime edo]]. 886edo, which doubles it, gives a good correction until the 11-limit.

==Regular temperament properties==

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

! rowspan="2" |[[Subgroup]]

! rowspan="2" | [[Subgroup]]

! rowspan="2" |[[Comma list|Comma List]]

! rowspan="2" | [[Comma list|Comma List]]

! rowspan="2" |[[Mapping]]

! rowspan="2" | [[Mapping]]

! rowspan="2" |Optimal 8ve Stretch (¢)

! rowspan="2" | Optimal 8ve Stretch (¢)

! colspan="2" |Tuning Error

! colspan="2" | Tuning Error

|-

![[TE error|Absolute]] (¢)

! [[TE error|Absolute]] (¢)

![[TE simple badness|Relative]] (%)

! [[TE simple badness|Relative]] (%)

|-

|2.3

| 2.3

|{{monzo|-702 443}}

| {{monzo|-702 443}}

|{{~~val~~|443 702}}

| {{mapping| 443 702 }}

| 0.1183

Line 31:

Line 36:

|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator~~ (reduced)~~

! Generator*

! Cents~~ (reduced)~~

! Cents*

! Associated ~~ratio~~

! Associated Ratio*

! Temperaments

|-

|1

| 1

|92\443

| 92\443

|249.21

| 249.21

|81/70

| 15/13

|[[Hemischis]] (~~7-limit~~)

| [[Hemischis]] (443)

|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

== Music ==

; [[User:Francium|Francium]]

* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] | [https://francium223.bandcamp.com/track/confusion Bandcamp] | [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|443}}
 == Theory ==
-et tempers out 67108864/66976875, [[6144/6125]] and [[32805/32768]] in the 7-limit; 806736/805255, 35156250/35153041, 759375/758912, [[131072/130977]], [[540/539]], 184549376/184528125, [[5632/5625]], [[8019/8000]], 160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172 and 20614528/20588575 in the 11-limit.
+edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1|5]] is quite large. To start with, the [[patent val]] {{val| 443 702 '''1029''' '''1244''' '''1533''' }} as well as the 443cde [[val]] {{val| 443 702 '''1028''' '''1243''' '''1532''' }} are worth considering.
-===Prime harmonics===
+Using the patent val, the equal temperament [[tempering out|tempers out]] [[6144/6125]], [[32805/32768]], and 67108864/66976875 in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]], and [[131072/130977]] in the 11-limit. It [[support]]s [[hemischis]], the 130 & 313 temperament.
+=== Prime harmonics ===
 {{Harmonics in equal|443}}
-===Subsets and supersets===
+=== Subsets and supersets ===
 edo is the 86th [[prime edo]]. 886edo, which doubles it, gives a good correction until the 11-limit.
-==Regular temperament properties==
+== Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" |[[Comma list|Comma List]]
+! rowspan="2" | [[Comma list|Comma List]]
-! rowspan="2" |[[Mapping]]
+! rowspan="2" | [[Mapping]]
-! rowspan="2" |Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br>8ve Stretch (¢)
-! colspan="2" |Tuning Error
+! colspan="2" | Tuning Error
 |-
-![[TE error|Absolute]] (¢)
+! [[TE error|Absolute]] (¢)
-![[TE simple badness|Relative]] (%)
+! [[TE simple badness|Relative]] (%)
 |-
-|2.3
+| 2.3
-|{{monzo|-702 443}}
+| {{monzo|-702 443}}
-|{{val|443 702}}
+| {{mapping| 443 702 }}
 | 0.1183
 | 0.1183
@@ Line 31: / Line 36: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(reduced)
+! Generator*
-! Cents<br>(reduced)
+! Cents*
-! Associated<br>ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
-|1
+| 1
-|92\443
+| 92\443
-|249.21
+| 249.21
-|81/70
+| 15/13
-|[[Hemischis]] (7-limit)
+| [[Hemischis]] (443)
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
 == Music ==
 ; [[User:Francium|Francium]]
 * "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] | [https://francium223.bandcamp.com/track/confusion Bandcamp] | [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning